Linear transceiver design for a MIMO interfering broadcast channel achieving max-min fairness

Meisam Razaviyayn, Mingyi Hong, Zhi-Quan Luo
2011 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)  
We consider the problem of linear transceiver design to achieve max-min fairness in a downlink MIMO multicell network. This problem can be formulated as maximizing the minimum rate among all the users in an interfering broadcast channel (IBC). In this paper we show that when the number of antennas is at least two at each of the transmitters and the receivers, the min rate maximization problem is NP-hard in the number of users. Moreover, we develop a low-complexity algorithm for this problem by
more » ... teratively solving a sequence of convex subproblems, and establish its global convergence to a stationary point of the original minimum rate maximization problem. Numerical simulations show that this algorithm is efficient in achieving fairness among all the users. I. INTRODUCTION We consider the linear transceiver design problem in a MIMO-IBC, in which a set of Base Stations (BSs) send data to their intended users. Both the BSs and the users are equipped with multiple antennas, and they share the same time/frequency resource for transmission. The objective is to maximize the minimum rate among all the users in the network, in order to achieve network-wide fairness. Providing max-min fairness has long been considered as an important design criterion for wireless networks. Hence various algorithms that optimize the min-rate utility in different network settings have been proposed in the literature. References [20] , [21] are early works that studied the max-min signal to interference plus noise ratio (SINR) power control problem and a related SINR feasibility problem in a scalar interference channel (IC). It was shown in [20], [21] that for randomly generated scalar ICs, with probability one there exists a unique optimal solution to the max-min problem. The proposed algorithm with an additional binary search can be used to solve the max-min fairness problem efficiently. Recently reference [17] derived a set of algorithms based on nonlinear Perron-Frobenius theory for the same network setting. Differently from [20], [21], the proposed algorithms can also deal with individual users' power constraints. Apart from the scalar IC case, there have been many published results [1], [3], [4], [8], [14], [18], [19] on the min rate maximization problem in a multiple input single output (MISO) network, in which the BSs are equipped with multiple antennas and the users are only equipped with a single antenna. Reference [19] utilized the nonnegnative matrix theory to study the related power control problem when the beamformers are known and fixed. When optimizing the transmit power and the beamformers jointly, M. Razaviyayn, M. Hong, and Z.-Q. Luo are with the
doi:10.1109/acssc.2011.6190228 dblp:conf/acssc/RazaviyaynHL11 fatcat:tbeprnre4fcehm4bojczb7m5ia